Factoring Radicals - Math

Begin by multiplying the numerator and denominator by the complement of the denominator:

Combine like terms and simplify:

To solve this equation, we have to factor our radicals. We do this by finding numbers that multiply to give us the number within the radical.

Add them together:

4 is a perfect square, so we can find the root:

Since both have the same radical, we can combine them:

Use the multiplication property of radicals to split the fourth roots as follows:

Simplify the new roots:

Begin by factoring the integer:

Now, simplify the exponents:

Begin by converting the radical into exponent form:

Now, multiply the exponents:

Begin by converting the radical into exponent form:

Now, combine the bases:

Simplify the integer:

Now, simplify the exponents:

Convert back into radical form and simplify:

Begin by using the FOIL method (First Outer Inner Last) to expand the expression.

Now, combine like terms:

Begin by multiplying the numerator and denominator by the complement of the denominator:

Use the FOIL method to multiply the radicals. F (first) O (outer) I (inner) L (last)

Now, combine like terms:

Simplify:

Begin by factoring the radicals:

Combine like terms:

Multiply the left side by and the right side by

Begin by converting the radicals into exponent form:

Now, combine the bases:

Convert back into radical form and simplify:

Begin by simplifying the right side of the rational expression:

Now, combine like terms:

Begin by using the FOIL method to multiply the radical expression. F (first) O (outer) I (inner) L (last)

Now, combine like terms:

Begin by multiplying the numerator and denominator by :

The expression cannot be further simplified.

Begin by factoring the radicals and combining like terms:

Multiply the left side of the equation by and the right side by :

Begin by factoring the integer:

Factor the exponents:

Begin by factoring the integer:

Factor the exponents:

Begin by factoring the integer:

Factor the exponents:

Begin by factoring the expression:

Now, take the square root:

Simplify the radical expression:

First, factor the coefficient:

It's definitely not obvious that 13 goes into 117 unless you examine the potential answers.

We can see that we have a group of two 2's, and a group of two 3's, so those will be on the outside of the radical. We also have 13 leftover.

Now we can look at the variables. We have which can easily be re-written as . This means that when we take the square root we'll get .

We have which can almost just as easily be written as , which is helpful because 90 is an even number. That can be re-written as , so when we take the square root we will get with one leftover.

Putting this all together gives: